How do you use the zero product property to solve a quadratic equation in factored form?.

In the word problem the number of the adult ticket is 225.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here total number of tickets = 516.

Which is contains adult and students tickets. Then let us take x is number of adult ticket and y is number of student tickets then,

=> x + y = 516 ------> 1

Now  there were 66 more student tickets sold than adult tickets then

=> y = x+66 -----> 2

Now put 2 into 1 then

=> x+66+x = 516

=> 2x = 516-66 = 450

=> x = 225.

Now put x = 225 into then

=> y = 225+66 = 291.

Hence the number of adult tickets is 291.

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The inverse of 7 is 1/7.

A reciprocal is one of a pair of numbers that when multiplied with another number equals the number 1.

The reciprocal of a and 1/a.

For example, if we have the number 7, the multiplicative inverse, or reciprocal, would be 1/7 because when you multiply 7 and 1/7 together, you get 1.

Multiplicative inverse:

The multiplicative inverse of a number can either be expressed as a fraction or as a number raised to the power of a negative one. A number multiplied by its multiplicative inverse is one.

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Using factoring, we do the following actions to make rational expressions simpler:

As much as you can, factor the numerator and denominator. Any factors that appear in both the numerator and the denominator should be eliminated. Your expression gets simplified as a result. How is an expression factorized:

Step 1 is to identify the expression's prime factors.

Step 2: Find the GCF by enclosing the common factors.

Write each term in the expression as a combination of the GCF and the final factor in step 3.

Step 4: Simplify the equation by applying the distributive property.

Y=12(x-6)(x+2) is an illustration of a quadratic function in factored form. This shape can be examined to determine the vertex as well as the graph's x-intercepts.

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Inequality can be used to determine x, the greatest number of 120-kilogram crates that can be loaded onto the shipping container is  8000 + 120C <= 27500

An inequality is a relationship that allows us to contrast two or more mathematical expressions.

Knowing that;

Each carton weighs 120 kg.

The container's maximum weight when loaded is 27500 kg.

Weight of the container as it is currently loaded: 8000 kg

Now that we have merged, we have;

Solution

because 8000 grams have already been loaded kilograms

into the container

each crate weighs 120 kilograms.

so 8000 + 120C <= 27500

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Research plan is a short document, which sets out initial thoughts on a research project in a logical and concise manner.

A research plan is the main part of a grant application and describes a principal investigator's proposed research.

A research plan is a short document, which sets out initial thoughts on a research project in a logical and concise manner.

We write a research plan by given steps.

Define the project purpose.

Identify individual objectives.

Select a research method.

Recruit participants and allocate tasks.

Prepare a project summary.

Create a realistic timeline.

Determine how to present your results.

The bibliographic information has Author name, Title of publication., Article title (if using a journal), Date of publication, Place of publication., Publisher, Volume number of a journal, magazine or encyclopedia and

Page number(s)

Hence, research plan is a short document, which sets out initial thoughts on a research project in a logical and concise manner.

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Complex fractions are called complex because they contain one or more fractions within the numerator and/or denominator of the fraction. These fractions within the fraction make the fraction more complex or difficult to simplify than a regular fraction, which only has a single numerator and denominator.

The term "complex" in mathematics often refers to something that is composed of multiple parts or layers, and that requires more steps or understanding to work with or solve.

In this case, the presence of one or more fractions within the fraction makes it more complex than a regular fraction, hence the name "complex fraction."

Another reason for the term complex is that the fractions in the numerator and denominator may have different or even the same variables, making it difficult to cancel them or simplify the expression.

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The graph that depicts a function is graph when the vertical line test is used (b).

By visually counting the number of times the curve crosses vertical lines, the vertical line test is a graphical approach for verifying whether a curve in the plane accurately depicts the graph of a function. the graph of a function can only be intersected by any vertical line in the plane once as a result.

A graph must satisfy the vertical line test in order to be considered a function representation. The vertical line test requires that the line from the x-axis only once crosses an associated y-value.

Graphs (a), (c), and (e) fail the vertical line test, indicating that they do not reflect a function.

So, graph is the name of the graph that represents a function (b)

The complete question is:

Use the vertical- line Test to determine which graph represents a function? I'm thinking it's the first one...

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Keiha sells computer software she sells 1800 if no books are sold.

Let y signify her overall salary (in dollars).

Let x be the volume of History is Fun that she sells.

Keep in mind that a change can be an improvement or a problem. Use a positive number to indicate an increase. Use a negative integer to indicate a reduction.

Consider the case when the equation =y+180070x connects x and y.

The number of books sold will affect the variable 70x in equation y=1800 + 70x.

Y=70x+1800=70(0)+1800=1800 if no books are sold.

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Full question

Keiko is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of History is Fun she sells. Suppose that x and y are related by the equation 2200 + 90x = y. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.

What is the change in Keiko's total pay for each copy of History is Fun she sells?

The orange bookmarks that Mateo can make than aqua bookmarks is 1.

Based on the information given, let x = number of aqua bookmarks

(1/6) × x = 3/4

x = (3/4) × (6/1)

x = 18/4

x = 4.5

Rounding down shows that we can make 4 aqua bookmarks.

y = number of orange bookmarks

(1/6)y = 9/10

y = (9/10)*(6/1)

y = 54/10

y = 5.4

This rounds down to 5 orange bookmarks.

Therefore, Mateo can make 5-4 = 1 extra orange bookmark compared to aqua.

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Mateo is making bookmarks with different colored ribbon. The

amount of each color he has is shown in the table. Each bookmark

will be yard long. How many more orange bookmarks can he make

than aqua bookmarks?

Table:

Color: Length (yd):

———————————-

Aqua. 3/4

Orange. 9/10

Yellow. 15/16

The equation y = 2x + 5 is already in standard form.

Standard form of a linear equation is Ax + By = C, where A, B, and C are constants and A and B cannot be both zero. In this case, A=2, B=1 and C=5, which meets the standard form equation, y = 2x + 5 is already in standard form.

Answer: y = 2x + 5 in standard form is 2x - y = -5

Step-by-step explanation: I hope this helps!

The height of the building is given as follows:

36 ft.

In this problem, we have two similar triangles, meaning that their side lengths are proportional.

As the triangles are similar, the equation involving proportions for the equivalent side lengths is given as follows:

x/6 = 45/7.5.

Applying the division on the right side of the equality, we have that:

45/7.5 = 6.

Hence:

x/6 = 6.

Applying cross multiplication, the height is given as follows:

x = 6(6) = 36 ft.

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The inequality that represents the amount of money Shenelle can spend on snacks is given as follows:

x + 10.25 ≤ 25.

The solution to the inequality is of:

x ≤ 14.75.

Meaning that she can spend at most $14.75 on the snacks.

The total amount that Shenelle has is given as follows:

$25.

Her spendings are given as follows:

Hence the inequality is given as follows:

x + 10.25 ≤ 25.

The solution is obtained as follows:

x ≤ 25 - 10.25.

x ≤ 14.75.

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Answer:

Step-by-step explanation:

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The given equation y = -3x + 5 has infinitely many solutions.

We have linear equation y = -3x + 5

We need to encounter how many solutions can satisfy the given equation. 

We know that,

y = -3x + 5 is a linear equation in two variables in the form ax + by + c = 0

For x = 0, y = 0 + 5 = 5. Therefore, (0, 5) is one solution.

For x = 1, y = -3 × 1 + 5 = 2. Therefore, (1, 2) is another solution.

For y = 0, -3x + 5 = 0, x = 5/3. Therefore, (5/3, 0) is another solution.

Clearly, for different values of x, we get different values for y. Thus, any value substituted in the place of x in the given equation will form another solution for the given equation. So, there is no limitation to the number of different solutions obtained by substituting real values for x in the given linear equation. Thus, a linear equation in two variables can have infinitely many solutions.

Thus, y = -3x + 5 has infinitely many solutions.

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The solution to the system of equations is y equals 1. 5 x 4 and y equals negative x is-= (1.6,-1.6)

In this case option A is correct

The coordinates of the ordered pair (s) that satisfy all of the equations in the system are the solution set to a system of equations. To put it another way, those x and y values will make the equations true. As a result, when a system of equations is graphed, the intersection points of the graphs are the system's solution.

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What is the solution to the system of equations y equals 1. 5 x 4 and y equals negative x?.

The solution sets are called algebraic sets.

An algebraic set is the locus of zeros of a collection of polynomials, and it is the set of solutions.

A solution set is a set of values that satisfy a given set of equations or inequalities.

The set containing all the solutions of an equation is called the solution set for that equation. If an equation has no solutions, we write ∅ for the solution set. ∅ means the null set.

A linear system with a unique solution has a solution set with one element. Solution sets are a challenge to describe only when they contain many elements.

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Answer: Positive

Hope this helps :)

Step-by-step explanation:

When multiplying or dividing with two negative numbers, the product/quotient will always be positive.

-8/-4 = 2

Answer: Positive

Step-by-step explanation:

Example for multiplication:

Imagine 4 friends that owe you $8 each.

Each friend that pays you back represents their payback as -$8.

-$8 * 4 friends = -$32 that they owe you.

The moment they give it back, you now have +$32. The Debt was taken away.

Example for Division:

Imagine splitting 8 dollars in debt with 4 friends, each friend then has $2 in debt. Each payback means you have +$2.

Another visual way to think of this is with Number Lines.

On a number line, when you multiply by a larger absolute value the numbers get bigger and go farther away from 0. So, taking a negative and multiplying it by a positive makes it MORE negative, as opposed to multiplying it by negative and then it reflects the number line,

Possible way in which two consecutive odd numbers are added to sum of 2023 is by evaluation using the formula (2n - 1) + (2n + 1) = 2023, so that we have 1010.5 + 1012.5 = 2023

Consecutive odd numbers are a sequence of numbers that are separated by a difference of 2 and are all odd numbers. For example the first four odd numbers are: 1, 3, 5, and 7. Odd numbers can be generated using the formula 2n -1.

We shall represent the first odd number with (2n - 1) so that the two consecutive odd numbers will be expressed as:

(2n - 1) + (2n + 1) = 2023

2n + 2n = 2023

4n = 2023

n = 2023/4 {divide through by 4}

n = 505.75

Therefore the two consecutive odd numbers added to sum of 2023 are derived as:

2(505.75) - 1 = 1010.5 and 2(505.75) + 1 = 1012.5

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Answer: Well, let’s consider a number, [math]n[/math], it could be even or odd, it doesn’t ...

Step-by-step explanation:

The inverse operations can be graphed by determining the inverse of the function by swapping the x and y variables,

Not all functions have inverses, and in order for a function to have an inverse, it must be a one-to-one function that is, there must not be repeated output for many inputs which indicates that not all functions have inverses. The various steps to graph inverse functions can be noted as -

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Answer:

72.5 / 2.5 = 29

29 - 8 = 21

21 / 3 = 7

7

Step-by-step explanation:

Answer:

b.

Step-by-step explanation:

5x ≥ 15 or x + 4 > 13

5x ≥ 15

x ≥ 15/5

x ≥ 3

x + 4 > 13

x > 13-4

x > 9.

So, the answer is x ≥ 3

So, in 4 years, there will be 1176 people attending.

To find out how many people will be attending in 4 years, you need to determine the total decrease in attendance over that time period. The attendance is decreasing at a rate of 0.5% per year, so over 4 years, the decrease in attendance will be 4 years x 0.5% = 2%

To find out how many people will be attending in 4 years, you can then subtract the 2% decrease from the current attendance of 1200 people:

1200 x (1 - 0.02) = 1176 people

So, in 4 years, there will be 1176 people attending.

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You must ascertain the overall drop in attendance over that time span in order to calculate the number of attendees in 4 years. If enrollment drops by 0.5% annually, it will drop by 2% over the course of four years (4 years x 0.5%).

Then, from the present attendance of 1200 people, subtract the 2% decline to determine how many attendees there will be in 4 years:

1200 times (1-0.02) ≈ 1176 individuals

Therefore, there will be 1176 attendees in 4 years.

Answer:

0.52

Step-by-step explanation:

25-12=13

boys are equal to 13

the probability of picking a boy at random will be;

13/25=0.52

No, it is not possible to draw a triangle.

This will be done by the property: the sum of two sides of a triangle should be more than the third side.

(6cm + 8cm) =15cm

14cm = 15cm

LHS<RHS

A triangle is not possible.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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The piecewise function will be written as y= -x { x < 0 } and y = x { x > 0 }.

A piecewise-defined function (also known as a piecewise function or a hybrid function) is a function defined by multiple sub-functions, each of which applies to a different interval of the main function's domain (a sub-domain).

Given that the function is f(x)= x. The piecewise function of the given function will vary from x being less than zero and x being greater than zero. The function can be written as  y= -x { x < 0 } and y = x { x > 0 }.

The graph of the piecewise function of the given function is attached with the answer below.

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Answer:

54 Hours

Step-by-step explanation:

first of all 540-54 he started with is 486 and 486/9 is 54 since you get 9 per hour

Answer: 54 Hours of babysitting

Step-by-step explanation: 540-54=486 Then you take 486 and you divide it by 9 to see how many hours you have to work and that would be 54 hours.

The experimental probability that the next customer to come into Chandler's boutique wears a size small is; 1/19

Theoretical probability is defined as the term used to describe what we expect to happen based on math theory, while experimental probability refers to what actually happens when the actual situation is tried out as an experiment.

In this question, we are given;

Number of small wears = 3

Number of medium wears = 32

Number of large wears = 22

Thus;

Total number of wears = 3 + 32 + 22

= 57

Probability that next customer wears small size = 3/57 = 1/19

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The correct expression to solve te sum of polynomials is [(-3x)+(-8x)]+4x+[9+5] (D).

To solve any polynomials problems, it is important for us to take a close look on the orders of each number. For the sum and substraction operation, we need to categorize each number based on its orders.

From the case, we have a problem as:

(9 - 3x²) + (-8x² + 4x  + 5)

We can categorize each order:

Order 2 = (-3x²) and (-8x²)

Order 1 = 4x

Order 0 = 9 and 5

Hence, we can solve the problem as:

(9 - 3x²) + (-8x² + 4x + 5)

= [(-3x²) + (-8x²)] + 4x + (9 + 5)

= -11x² + 4x + 14

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The commutative property applies only to addition and multiplication of real numbers.

What is commutative property in math?

This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer. Subtraction and division are NOT commutative.

The commutative property of real numbers states that for any real numbers a and b, a + b = b + a and a * b = b * a. In other words, the order in which two real numbers are added or multiplied does not change the result. This property applies to both addition and multiplication of real numbers.

Therefore, the commutative property applies only to addition and multiplication of real numbers.

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